We review the basics of and extract some key insights from these results in the following subsections. Building on those, in Sec. REF  we prove a necessary and sufficient criterion for bipartite entanglement. In Sec. REF  we show that this, too, can be recast as a compatibility condition with respect to time orientations. Our work opens up various directions for future research, including practical considerations of our entanglement criterion as well as its generalisation to von Neumann algebras [1]} (see Sec. REF  and Sec. ).
